Solve the initial value problems dy 19. (x + 1)- dx -2(x² + x)y=x+1' x>-1, y(0) = 5 dy 17. 0 + y = sin 0, 0, y(π/2) = 1 de en

Q: Find the area of the region bounded by the curves 1 y = (x+6)²¹ Y = 4 and the x-axis using vertical…

A: Given problem is :

Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(9y) dy =…

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Q: Evaluate: xy² dx dy S

A: Given: ∫04∫0yxy2dxdy

Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: Given : Let I be a proper ideal of the commutative ring R with identity. Then I is a _______ if and…

Q: Solve the differential equation. x dy dx = y + x³ + 3x² -2 x

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Q: 62. y" +9y=e* cosx

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Q: (x² - y²)²] 1²₁ 1² du du dt x+y Evaluate: ₁ S

A: Given ∫-13∫02x2-y22x+ydudt Since x2-y22x+y is constant with respective u and t, we take constant out…

Q: show that $(x, y, z) = PDE : 2²4 8²4 дуг дуг + 1 2 x² + y² + z² 824 dz² satisfies the

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Q: 7. The value of sin(1¹/3) dt 12/3 S

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Q: an+1 Suppose that an ∞ Σ απ( – 81)" man n=1 →1 as n→ ∞o. Find the radius of convergence.

A: Explanation of the answer is as follows

Q: (5) If f(x) =.... then f(x) is reducible in Z5[x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x² + 2

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Q: It is given that the radius of the semicircle increases at the rate of 0.5 cms -1 when heated.…

A: Given ,  The radius of the semicircle increases at the rate of 0.5 cm s-1 when heated We have to…

Q: Find the area of the surface obtained by rotating the curve y = cos(2x), 0≤ x ≤ π/6, about the…

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Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

A: Given

Q: Q8. Solve the following D.E to find y as a function of x : dy dx y sin 2x 3y² cos2x

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Q: π/3 So, f²ef/³ t In u tans ds du dt

A: Given problem:-

Q: ./ which expression best to describe 31% ? (a) Just under a half (b) A tiny fraction (c) Nearly a…

A: Given data÷

Q: 10) y7 exbx

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Q: let f(x)=x +9x-1 if (f o g)(x)=x+9√x-1. find g(x)

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Q: Evaluate the following double integral over the region R by converting it to an iterated integral.…

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Q: - 2.f(x,y) = y²x¹ey.

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Let f : R 7−→ R be defined by f(x) = 2 − 5x. Show that f is bijective, and find f^(−1)(x).

A: Let f:R→R be defined by f(x) = 2 - 5x.

Q: Flag question Evaluate: ³²₁ [2³(x + y)³] dz dy dx

A: Let's evaluate given triple integral.

Q: q-Sin ²1x1 1²/x/_alx

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Q: Find the solution of the given initial value problem. ty+3y=t²t+5, y(1) = 2, t> 0 11

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Q: Question 1 Express the Laplace Transform of the following functions: (a) f(t) = 2e5t sinh(7t) — t8…

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Q: cln 3 In In 2 tanh xsech’x_dx

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Q: Q9. If W = f(u)=u' + sinu+Inu, and a=ax+by, where a, and b are constants, show that aw aw b. ax

A: We have to prove the given statement.

Q: Differentiate the function. P(w) = 2w² - 6w + 4 W

A: Given function is differentiated.

Q: please do the second (b)

A: Let's find volume when rotated about y axis.

Q: 2 ³₁²₁²[z³(x + y)³] dz dy dx -4 J

A: In this question we have to solve the given triple integral.

Q: Evaluate: ƒ³₁ ƒ²₁ √√²[z³(x + y)³] dz dy dx

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Q: t sin (=) dt du

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Q: Evaluate the integral: f/2 sin(4t-u) du dt

A: To evaluate: ∫π2π∫0tsin(4t-u) du dt

Q: = 10. Find a second-degree polynomial P such that P(1) = 7, P'(1) = 7, and P"(1) P(x) = Need Help?…

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Q: Evaluate [x² √2x+1dx

A: Indefinite Integration

Q: 70. 4y" +5y' - 2y = e²+xsinx

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Q: 9) y = вод по- 10) У th 4x 1+₂x exbx

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 2. I. -4 1 Evaluate each determinant. 3 -3

A: -431-3=12-3

Q: aluate the line integral y dx + xy dy where C is the rectangle with vert 0), (5, 4), and (0,4).

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Q: 6 By separation of variables, Solve the following 5 PDES :- учи ²4 dx2 0 o u(e,t) = u(5,t) =6 u(x,0)…

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Q: 5.) I. -2 -3 -6 2 Simplify. Write "undefined -4 6 0 +

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Q: 8. The value of ve A. sin-1 (e) + C C. sin-1 (e-x) + C dx B. -sin-1 (e-2x) + C D. sin-1 (e-2x) + C

A: Topic = Integration Correct option = A

Q: Evaluate the following * [csc² cot (5x+6)/2 + C cot(5x+6)/ 5+ C - cot(5x+6)/ 5+ C cot(5x-6)/ 5+ C…

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Q: A- Answer the following L-1 3s-1 s²+2s+5

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: To find the volume of the solid that results when the shaded region is revolved about the indicated…

Q: 3 -2 Evaluate: ₂₁ [2³(x + y)³] dz dy dx

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Q: Determine y = Yc+yp using Non-homogenous equations: Method of Undetermined Coefficients Given: y" +…

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Q: -2 -t² rln s Evaluate the integral: 5² 5²² n fote" du ds dt

A: We have to evaluate the integral ∫12∫tt2∫0ln st eu du ds dt.

Q: Determine the general solution of y" - y = 0 given y₁(x) = e e-2x using reduction of order

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